Synchrony in neural circuits has been implicated in cognitive functions such as attention, working memory and retrieval and encoding of information, and abnormal synchrony has been implicated in psychiatric and neurological disorders. Neural oscillations are comprised of synchronous activity of a population of neurons. Neural oscillators can be implemented at the level of single oscillatory neurons, or at the level of a network of excitable elements. Electrical signaling in single neurons can be modeled using an electrical equivalent circuit comprised of linear and nonlinear conductances in parallel with a membrane capacitance. The tendency of oscillators to synchronize can be predicted using phase response curves, which plot the amount that an oscillation cycle is lengthened or shortened by a perturbation. The synchronization tendencies depend on the nonlinear dynamics of the neurons, specifically whether they integrate their inputs or resonate to a preferred frequency. Here we define criteria for synchronization of a population of all-to-all coupled identical neurons, and explain how this synchrony might be preserved in a population of noisy, sparsely firing heterogeneous neurons.
Professor and Vice Chair for Research